How to Calculate the Total Resistance in a Circuit?

[[KNIGHT]]

Homework Statement

Calculate the total resistance of the 2 circuits given below

Homework Equations

R = R1+R2+R3...
(1/R) = (1/R1) + (1/R2) + (1/R3) + ....

The Attempt at a Solution

I am unable to understand how to obtain the final resistance

 

[Doc Al]

General strategy: Look for pairs of resistors that are purely in parallel or in series. Then replace those pairs with their equivalent resistance. Then do it again, until you've simplified it enough.

 

[[KNIGHT]]

After following what you said i got 25/84 Ohms as the answer for the 2nd circuit. Is it correct?

But the 1st one is still confusing because of the connection in between

 

[Susagep]

Homework Statement

Calculate the total resistance of the 2 circuits given below

Homework Equations

R = R1+R2+R3...
(1/R) = (1/R1) + (1/R2) + (1/R3) + ....

The Attempt at a Solution

I am unable to understand how to obtain the final resistance

Answer to Circuit # 2

Rt = R1 * R2 / R1 + R2

Give arbitrary values to each resistance, for example 100 Ohms each. Find a parallel pair and evaluate:Example 2 parallel resistor [Items 1 & 2] 100 Ohms each equals 50 Ohms, that is 100 Ohms divided by 2 resistors. Now add that value to the next resistor in series [ Item 4], you now have 150 Ohms. Find the series branch and add the resistance which equal 200 Ohms Item 7 & 5]. You now have 150 Ohms in parallel with 200 Ohms, evaluate them both in parallel and you arrived at a value of 85.714 Ohms for the entire circuit. Follow the same procedure for circuit # 1

 

[gneill]

After following what you said i got 25/84 Ohms as the answer for the 2nd circuit. Is it correct?

It looks like you've forgotten to take a reciprocal somewhere. Check your work, or better yet, post it here so others can check.

But the 1st one is still confusing because of the connection in between

Can you identify any candidates for parallel or serial connections?

 

[[KNIGHT]]

It looks like you've forgotten to take a reciprocal somewhere

Thanks for pointing it out. I have made a simplification error. So the answer is 84/25 Ohms. Is it correct now?

Can you identify any candidates for parallel or serial connections?

Can i consider 3 & 2 as the 1st pair of parallel resistors and 6 & 7 as the 2nd pair of parallel resistors.
Thereafter should i add the 1st and 2nd pair in series?

Btw its the resistance values that are marked in the diagram

 

[gneill]

Thanks for pointing it out. I have made a simplification error. So the answer is 84/25 Ohms. Is it correct now?

Yes, the result is correct. I cannot comment on your methodology since you did not show it.

 

[[KNIGHT]]

Here is the way i did it
considered 1 & 2 as a parallel pair and found their resistance and added it in series with 4. (group 1)
Then i added 7 & 5 in series and considered it as group 2.
The final answer was obtained by adding group 1 and 2 in parallel

 

[gneill]

Here is the way i did it
considered 1 & 2 as a parallel pair and found their resistance and added it in series with 4. (group 1)
Then i added 7 & 5 in series and considered it as group 2.
The final answer was obtained by adding group 1 and 2 in parallel

Yes, that is a correct method.

 

[[KNIGHT]]

What about the method to solve the 1st first? Is it correct?

 

[gneill]

What about the method to solve the 1st first? Is it correct?

You'll have to be more explicit.

Any correct method should arrive at the same result...

 

[Doc Al]

What about the method to solve the 1st first? Is it correct?

Yes. Assuming that this was your method for the 1st circuit:

Can i consider 3 & 2 as the 1st pair of parallel resistors and 6 & 7 as the 2nd pair of parallel resistors.
Thereafter should i add the 1st and 2nd pair in series?

That is a good approach.